3D Equivalent Space-Varying Permeability Model of HTS Bulks for Computation of Electromagnetic Forces

This paper proposes a novel methodology for calculating a space-varying permeability in HTS bulks, ensuring the same magnetic energy stored in E-J models at each infinitesimal volume. This stationary model is applied for the electromagnetic force calculation in HTS bulks. For the design of HTS bulk machines, multi-objective optimization is necessary to have accurate results. However, due to the nonlinear nature of HTS bulks finite element, Finite Element Analysis (FEA) simulations for optimization are heavily time consuming, even using 2D models, making this approach “infeasible.” The use of equivalent models that guarantee precise results with shorter computation times is then imperative. The method proposed is applied following two basic steps. First, the 3D finite element model is simulated without the bulk to obtain the spatial magnetic flux distribution in the volume where it should be. In the second step, the bulk is included, and the HTS magnetic flux density distribution is obtained using superconducting physics. From these, the HTS equivalent space-varying permeability is computed by the quotient of the two magnetic flux densities. With this, stationary and linear FEA simulations can now be easily performed for the computation of electromagnetic forces in design problems. The proposed method was validated using simulation and experimental tests based on YBCO/GdBCO permanent-magnet force interactions. These results show that, with a previous general study of the geometry to optimize, the equivalent model can be used for optimization purposes, greatly reducing the computational time.